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On uniformly rotating fluid drops trapped between two parallel plates

Kruse, H.-P. and Marsden, J. E. and Scheurle, J. (1993) On uniformly rotating fluid drops trapped between two parallel plates. In: Exploiting symmetry in applied and numerical analysis. Lectures in applied mathematics . No.29. American Mathematical Society , pp. 307-317. ISBN 0821811347.

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This contribution is about the dynamics of a liquid bridge between two fixed parallel plates. We consider a mathematical model and present some results from the doctoral thesis [10] of the first author. He showed that there is a Poisson bracket and a corresponding Hamiltonian, so that the model equations are in Hamiltonian form. The result generalizes previous results of Lewis et al. on the dynamics of free boundary problems for "free" liquid drops to the case of a drop between two parallel plates, including, especially the effect of capillarity and the angle of contact between the plates and the free fluid surface. Also, we prove the existence of special solutions which represent uniformly rotating fluid ridges, and we present specific stability conditions for these solutions. These results extend work of Concus and Finn [2] and Vogel [18],[19] on static capillarity problems (see also Finn [5]). Using the Hamiltonian structure of the model equations and symmetries of the solutions, the stability conditions can be derived in a systematic way. The ideas that are described will be useful for other situations involving capillarity and free boundary problems as well.

Item Type:Book Section
Additional Information:© 1993 American Mathematical Society. Partially supported by a Humboldt award at the University of Hamburg and by DOE Contract DE-FG03-88ER25064. This paper is in final form and no version of it will be submitted for publication elsewhere.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FGO3-88ER25064
Series Name:Lectures in applied mathematics
Issue or Number:29
Classification Code:1991 MSC:Primary 76B45, 76E05, 58F05, 58F10
Record Number:CaltechAUTHORS:20100924-075908242
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20116
Deposited By: Ruth Sustaita
Deposited On:24 Sep 2010 20:01
Last Modified:03 Oct 2019 02:06

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